Extensions 1→N→G→Q→1 with N=C₂₀ and Q=M₄(2)

Direct product G=N×Q with N=C₂₀ and Q=M₄(2)

		d	ρ	Label	ID
M₄(2)×C₂₀		160		M4(2)xC20	320,905

Semidirect products G=N:Q with N=C₂₀ and Q=M₄(2)

extension	φ:Q→Aut N	d	Label	ID
C₂₀⋊₁M₄(2) = C₂₀⋊M₄(2)	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	160	C20:1M4(2)	320,1043
C₂₀⋊₂M₄(2) = C₂₀⋊₂M₄(2)	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	160	C20:2M4(2)	320,1112
C₂₀⋊₃M₄(2) = C₂₀⋊₃M₄(2)	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	160	C20:3M4(2)	320,1019
C₂₀⋊₄M₄(2) = C₄×C₄.F₅	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	160	C20:4M4(2)	320,1015
C₂₀⋊₅M₄(2) = C₂₀⋊₅M₄(2)	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	160	C20:5M4(2)	320,464
C₂₀⋊₆M₄(2) = C₂₀⋊₆M₄(2)	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	160	C20:6M4(2)	320,465
C₂₀⋊₇M₄(2) = C₂₀⋊₇M₄(2)	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	160	C20:7M4(2)	320,639
C₂₀⋊₈M₄(2) = C₂₀⋊₈M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	160	C20:8M4(2)	320,1096
C₂₀⋊₉M₄(2) = C₄×C₂².F₅	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	160	C20:9M4(2)	320,1088
C₂₀⋊₁₀M₄(2) = C₈⋊₆D₂₀	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	160	C20:10M4(2)	320,315
C₂₀⋊₁₁M₄(2) = C₄×C₈⋊D₅	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	160	C20:11M4(2)	320,314
C₂₀⋊₁₂M₄(2) = C₅×C₈⋊₆D₄	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	160	C20:12M4(2)	320,937
C₂₀⋊₁₃M₄(2) = C₂₀⋊₁₃M₄(2)	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	160	C20:13M4(2)	320,551
C₂₀⋊₁₄M₄(2) = C₄×C₄.Dic₅	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	160	C20:14M4(2)	320,549
C₂₀⋊₁₅M₄(2) = C₅×C₄⋊M₄(2)	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	160	C20:15M4(2)	320,924

Non-split extensions G=N.Q with N=C₂₀ and Q=M₄(2)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁M₄(2) = D₂₀⋊C₈	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	160		C20.1M4(2)	320,209
C₂₀.₂M₄(2) = Dic₁₀⋊₁C₈	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	320		C20.2M4(2)	320,210
C₂₀.₃M₄(2) = Dic₅.₂₃D₈	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	160		C20.3M4(2)	320,262
C₂₀.₄M₄(2) = Dic₅.₁₂Q₁₆	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	320		C20.4M4(2)	320,268
C₂₀.₅M₄(2) = C₂₀.M₄(2)	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	320		C20.5M4(2)	320,1047
C₂₀.₆M₄(2) = C₂₀.₆M₄(2)	φ: M₄(2)/C₂ → C₂×C₄ ⊆ Aut C₂₀	320		C20.6M4(2)	320,1126
C₂₀.₇M₄(2) = C₄².₃F₅	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.7M4(2)	320,198
C₂₀.₈M₄(2) = C₄₀⋊₂C₈	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	320		C20.8M4(2)	320,219
C₂₀.₉M₄(2) = C₄₀⋊₁C₈	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	320		C20.9M4(2)	320,220
C₂₀.₁₀M₄(2) = C₂₀.₁₀M₄(2)	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	80	4	C20.10M4(2)	320,229
C₂₀.₁₁M₄(2) = C₄².₁₅F₅	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	160		C20.11M4(2)	320,1021
C₂₀.₁₂M₄(2) = C₂₀⋊C₁₆	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	320		C20.12M4(2)	320,196
C₂₀.₁₃M₄(2) = D₁₀⋊C₁₆	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	160		C20.13M4(2)	320,225
C₂₀.₁₄M₄(2) = C₄².₁₂F₅	φ: M₄(2)/C₄ → C₄ ⊆ Aut C₂₀	160		C20.14M4(2)	320,1018
C₂₀.₁₅M₄(2) = C₂₀.₅₃D₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	320		C20.15M4(2)	320,37
C₂₀.₁₆M₄(2) = C₂₀.₃₉SD₁₆	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	320		C20.16M4(2)	320,38
C₂₀.₁₇M₄(2) = D₂₀⋊₄C₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	160		C20.17M4(2)	320,41
C₂₀.₁₈M₄(2) = Dic₁₀⋊₄C₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	320		C20.18M4(2)	320,42
C₂₀.₁₉M₄(2) = C₈₀⋊C₄	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	80	4	C20.19M4(2)	320,70
C₂₀.₂₀M₄(2) = C₈.₂₅D₂₀	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	80	4	C20.20M4(2)	320,72
C₂₀.₂₁M₄(2) = C₂₀.₅₇D₈	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	160		C20.21M4(2)	320,92
C₂₀.₂₂M₄(2) = C₂₀.₂₆Q₁₆	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	320		C20.22M4(2)	320,93
C₂₀.₂₃M₄(2) = C₄².₁₉₈D₁₀	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	320		C20.23M4(2)	320,458
C₂₀.₂₄M₄(2) = C₄².₂₀₂D₁₀	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	160		C20.24M4(2)	320,462
C₂₀.₂₅M₄(2) = C₄².₂₁₀D₁₀	φ: M₄(2)/C₄ → C₂² ⊆ Aut C₂₀	320		C20.25M4(2)	320,651
C₂₀.₂₆M₄(2) = C₂₀.₂₆M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	320		C20.26M4(2)	320,221
C₂₀.₂₇M₄(2) = Dic₅.₁₃D₈	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	320		C20.27M4(2)	320,222
C₂₀.₂₈M₄(2) = C₂₀.₂₃C₄²	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	80	4	C20.28M4(2)	320,228
C₂₀.₂₉M₄(2) = C₂₀.₂₉M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	80	4	C20.29M4(2)	320,250
C₂₀.₃₀M₄(2) = C₂₀.₃₀M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	160		C20.30M4(2)	320,1097
C₂₀.₃₁M₄(2) = C₂₀.₃₁M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	320		C20.31M4(2)	320,218
C₂₀.₃₂M₄(2) = C₁₀.M₅(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	320		C20.32M4(2)	320,226
C₂₀.₃₃M₄(2) = C₁₀.₆M₅(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	160		C20.33M4(2)	320,249
C₂₀.₃₄M₄(2) = C₂₀.₃₄M₄(2)	φ: M₄(2)/C₂² → C₄ ⊆ Aut C₂₀	160		C20.34M4(2)	320,1092
C₂₀.₃₅M₄(2) = Dic₁₀⋊₃C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	320		C20.35M4(2)	320,14
C₂₀.₃₆M₄(2) = D₂₀⋊₃C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	160		C20.36M4(2)	320,17
C₂₀.₃₇M₄(2) = C₄₀⋊₁₁Q₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	320		C20.37M4(2)	320,306
C₂₀.₃₈M₄(2) = C₄₀⋊₈C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	320		C20.38M4(2)	320,13
C₂₀.₃₉M₄(2) = C₄₀.₈₈D₄	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	320		C20.39M4(2)	320,59
C₂₀.₄₀M₄(2) = D₁₀⋊₁C₁₆	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	160		C20.40M4(2)	320,65
C₂₀.₄₁M₄(2) = C₄².₂₈₂D₁₀	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	160		C20.41M4(2)	320,312
C₂₀.₄₂M₄(2) = C₅×D₄⋊C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	160		C20.42M4(2)	320,130
C₂₀.₄₃M₄(2) = C₅×Q₈⋊C₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	320		C20.43M4(2)	320,131
C₂₀.₄₄M₄(2) = C₅×C₈⋊₄Q₈	φ: M₄(2)/C₈ → C₂ ⊆ Aut C₂₀	320		C20.44M4(2)	320,947
C₂₀.₄₅M₄(2) = C₄₀⋊₆C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.45M4(2)	320,15
C₂₀.₄₆M₄(2) = C₄₀⋊₅C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.46M4(2)	320,16
C₂₀.₄₇M₄(2) = C₂₀.₄₅C₄²	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.47M4(2)	320,24
C₂₀.₄₈M₄(2) = C₄₀.D₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.48M4(2)	320,111
C₂₀.₄₉M₄(2) = C₄².₇Dic₅	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.49M4(2)	320,553
C₂₀.₅₀M₄(2) = C₄².₂₇₉D₁₀	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.50M4(2)	320,12
C₂₀.₅₁M₄(2) = C₂₀⋊₃C₁₆	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.51M4(2)	320,20
C₂₀.₅₂M₄(2) = C₄₀.₉₁D₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.52M4(2)	320,107
C₂₀.₅₃M₄(2) = C₄².₆Dic₅	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.53M4(2)	320,552
C₂₀.₅₄M₄(2) = C₅×C₈⋊₂C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.54M4(2)	320,139
C₂₀.₅₅M₄(2) = C₅×C₈⋊₁C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	320		C20.55M4(2)	320,140
C₂₀.₅₆M₄(2) = C₅×C₁₆⋊C₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.56M4(2)	320,152
C₂₀.₅₇M₄(2) = C₅×C₂³.C₈	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	80	4	C20.57M4(2)	320,154
C₂₀.₅₈M₄(2) = C₅×C₄².₆C₄	φ: M₄(2)/C₂×C₄ → C₂ ⊆ Aut C₂₀	160		C20.58M4(2)	320,933
C₂₀.₅₉M₄(2) = C₅×C₈⋊C₈	central extension (φ=1)	320		C20.59M4(2)	320,127
C₂₀.₆₀M₄(2) = C₅×C₂²⋊C₁₆	central extension (φ=1)	160		C20.60M4(2)	320,153
C₂₀.₆₁M₄(2) = C₅×C₄⋊C₁₆	central extension (φ=1)	320		C20.61M4(2)	320,168
C₂₀.₆₂M₄(2) = C₅×C₄².₁₂C₄	central extension (φ=1)	160		C20.62M4(2)	320,932

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Extensions 1→N→G→Q→1 with N=C20 and Q=M4(2)

Extensions 1→N→G→Q→1 with N=C₂₀ and Q=M₄(2)